Asymptotic propagations of asymptotical monostable type equations with shifting habitats

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Yi, Taishan¹  Chen, Yuming²  Wu, Jianhong³ 

[1] Sun Yat Sen Univ, Sch Math Zhuhai, Zhuhai 519082, Guangdong, Peoples R China

[2] Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada

[3] York Univ, Dept Math & Stat, Toronto, ON M3J 1P3, Canada

关键词: Asymptotic propagation;    Comparison principle;    Asymptotical monostable type equation;    Shifting habitat;    Unbalanced resource;   

DOI  :  10.1016/j.jde.2020.04.025

来源: Elsevier

【 摘 要 】

We consider the nonlinear propagation for a single species population in a shifting habitat subject to unbalanced resources. The population dynamics is modelled by a reaction-diffusion equation with an asymptoticalmonostable type nonlinearity. Complicated dynamical patterns, naturally depending on the velocity of the shifting resource and the propagation velocities of the limiting systems at both infinity and -infinity, emerge, and our focus is to characterize these patterns. We first characterize the persistence and extinction of an asymptotical Fisher-KPP type equation and then establish a key relationship between the asymptotical Fisher-KPP type and the asymptotical monostable type equations. These, together with comparison principles, enable us 1). to obtain asymptotic propagation behaviours of asymptotical monostable type equations and 2). to analyze and describe the influence of the velocity of the shifting resource and the propagation velocity of the limiting systems on the asymptotic propagations of the reaction-diffusion equation with an asymptotical monostable type nonlinearity. (C) 2020 Elsevier Inc. All rights reserved.

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